Equations () and () follows from Equation (REF ) with the help
of the well-known relations for the Gauss Hypergeometric Function (see [1]}):
\(F(1,-n-1;2n+4;-2)=\frac{1}{3}F(1,3n+5;2n+4;2/3)=\frac{2^{n+1}}{\binom{3n+4}{n+1}}\sum \limits _{k=0}^{n+1}\frac{\binom{3n+4}{k}}{2^k}.\) 
